x= 1/2-

[Max@Math Revolution]

[GMAT math practice question]

\(X=\frac{1}{2-\sqrt[3]{2}}\) . What is the value of 3x^3-6x^2+3x?

A. 1/2
B. 1
C. 3/2
D. 2
E. 5/2

[Max@Math Revolution]

=>

\(X=\frac{1}{2-\sqrt[3]{2}}\)

⇔ x(2- \(\sqrt[3]{2}\) )=1
⇔ 2x- \(\sqrt[3]{2}\) x=1
⇔ 2x-1= \(\sqrt[3]{2}\) x
⇔ (2x-1)^3=( \(\sqrt[3]{2}\) x)^3
⇔ 8x^3-12x^2+6x-1=2x^3
⇔ 6x^3-12x^2+6x-1=0
⇔ 6x^3-12x^2+6x=1
⇔ 3x^3-6x^2+3x=1/2

Therefore, A is the answer.
Answer: A